Vertex operators for quantum groups and application to integrable systems

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dc.creatorRagoucy, E.
dc.date2001-08-30
dc.date2002-07-26
dc.date.accessioned2026-07-07T10:54:16Z
dc.date.available2026-07-07T10:54:16Z
dc.descriptionStarting with any R-matrix with spectral parameter, obeying the Yang-Baxter equation and a unitarity condition, we construct the corresponding infinite dimensional quantum group U_{R} in term of a deformed oscillators algebra A_R. The realization we present is an infinite series, very similar to a vertex operator. Then, considering the integrable hierarchy naturally associated to A_{R}, we show that U_{R} provides its integrals of motion. The construction can be applied to any infinite dimensional quantum group, e.g. Yangians or elliptic quantum groups. Taking as an example the R-matrix of Y(N), the Yangian based on gl(N), we recover by this construction the nonlinear Schrodinger equation and its Y(N) symmetry.
dc.description19 pages, no figure, Latex2e Error in theorem 3.3 and lemma 3.1 corrected
dc.identifierhttps://arxiv.org/abs/math/0108207
dc.identifierhttp://arxiv.org/abs/math/0108207
dc.identifierJ.Phys.A35:7929-7942,2002
dc.identifierdoi:10.1088/0305-4470/35/37/305
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185753
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subject17B37; 81R12
dc.titleVertex operators for quantum groups and application to integrable systems
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